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620 Chapter 12 APPLICATIONS IN COMMUNICATIONS
FIGURE 12.10
Two types of distortion in the DM encoder
by a linear staircase function. In order for the approximation to be relatively
good, the waveform s (t)must change slowly relative to the sampling
rate. This requirement implies that the sampling rate must be several (a
factor of at least 5) times the Nyquist rate. A lowpass filter is usually
incorporated into the decoder to smooth out discontinuities in the reconstructed
signal.
12.4.1 ADAPTIVE DELTA MODULATION (ADM)
At any given sampling rate, the performance of the DM encoder is limited
by two types ofdistortion as shown in Figure 12.10. One is called slopeoverload
distortion. It is due to the use of a step size ∆ 1 that is too small to
follow portions of the waveform that have a steep slope. The second type
of distortion, called granular noise, results from using a step size that is too
large in parts of the waveform having a small slope. The need to minimize
both of these two types of distortion results in conflicting requirements in
the selection of the step size ∆ 1 .
An alternative solution is to employ a variable size that adapts itself
to the short-term characteristics of the source signal. That is, the step size
is increased when the waveform has a steep slope and decreased when the
waveform has a relatively small slope.
Avariety of methods can be used to set adaptively the step size in
every iteration. The quantized error sequence ẽ(n) provides a good indication
of the slope characteristics of the waveform being encoded. When the
quantized error ẽ(n) ischanging signs between successive iterations, this
is an indication that the slope of the waveform in the locality is relatively
small. On the other hand, when the waveform has a steep slope, successive
values of the error ẽ(n) are expected to have identical signs. From these observations
it is possible to devise algorithms that decrease or increase the
step size, depending on successive values of ẽ(n). A relatively simple rule
devised by [13] is to vary adaptively the step size according to the relation
∆(n) =∆(n − 1) Kẽ(n)ẽ(n−1) , n =1, 2,... (12.23)
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